- Email: [email protected]
Accuracy of Intraocular Lens Formulas in Eyes With Keratoconus
Journal Pre-proof Accuracy of intraocular lens formulas in eyes with keratoconus Kendrick M. Wang, Albert S. Jun, John G. Ladas, Aazim A. Siddiqui, Fasika Woreta, Divya Srikumaran PII:
S0002-9394(19)30576-8
DOI:
https://doi.org/10.1016/j.ajo.2019.11.019
Reference:
AJOPHT 11148
To appear in:
American Journal of Ophthalmology
Received Date: 12 August 2019 Revised Date:
11 November 2019
Accepted Date: 14 November 2019
Please cite this article as: Wang KM, Jun AS, Ladas JG, Siddiqui AA, Woreta F, Srikumaran D, Accuracy of intraocular lens formulas in eyes with keratoconus, American Journal of Ophthalmology (2019), doi: https://doi.org/10.1016/j.ajo.2019.11.019. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Elsevier Inc. All rights reserved.
Accuracy of intraocular lens formulas in eyes with keratoconus Short title: Accuracy of IOL formulas in eyes with keratoconus. Kendrick M Wang1, Albert S Jun1, John G Ladas1,2, Aazim A Siddiqui3, Fasika Woreta1, Divya Srikumaran1 1
Wilmer Eye Institute, Johns Hopkins University School of Medicine, 600 North Wolfe Street, Baltimore, MD 21287
2
Maryland Eye Consultants and Surgeons, 2101 Medical Park Drive, Suite 101, Silver Spring, MD 20902
3
Department of Ophthalmology and Visual Sciences, Montefiore Medical Center, Albert Einstein College of Medicine, 3332 Rochambeau Avenue, 3rd floor, Room 306, Bronx, NY 10467
Corresponding Author: Divya Srikumaran MD, Wilmer Eye Institute at Odenton, 1106 Annapolis Road, Suite 290, Odenton, MD 21113. Phone: (410) 874-1428. Email: [email protected]
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Introduction Keratoconus is a progressive non-inflammatory condition of the cornea characterized by corneal ectasia and thinning as well as the development of high irregular astigmatism. Patients with mild to moderate disease may achieve adequate visual acuity with spectacle correction, whereas those with advanced disease typically require contacts lenses. Calculation of intraocular lenses (IOLs) in patients with keratoconus can be challenging for a number of reasons, including the corneal abnormalities and deeper anterior chambers1 seen in these patients. Changes to the cornea typically include inferior steepening and apex thinning; however, steepening and thinning can occur throughout the cornea. Corneal changes in keratoconus influence the ratio between the anterior corneal curvature and posterior corneal curvature. This challenges the assumption that the Gullstrand schematic eye model is an appropriate model for the derivation of the standard keratometric index of refraction used by keratometers and corneal topographers. There is limited literature on the calculation of IOL power in eyes with keratoconus.2-8 All studies show that there tends to be a hyperopic error in IOL formulas that increases as keratoconus worsens.2,7-9 There also is a dearth of literature on which formula results in the most accurate IOL power prediction. Although some literature concludes that the SRK/T is the most accurate formula,3,6,9 other studies have recommended using the SRK/II formula in keratoconic eyes.3,8 Furthermore, there is a growing interest in using toric IOLs to treat astigmatism from keratoconus.2,3,6 Additionally, improving accuracy of IOL power predictions is especially needed in eyes that are preoperatively spectaclecorrected versus preoperatively contact-lens corrected. Eyes with keratoconus tend to be longer than normal eyes, with longer axial lengths and deeper anterior chamber depths.1 This affects the estimated lens position (ELP) and contributes to inaccuracy in prediction of IOL power. Optical biometry in patients with keratoconus is also a source of error for IOL power predictions. Watson et al.7 showed that optical biometry tends to overestimate corneal power, resulting in hyperopic outcomes due to inadequate power in the IOL implanted. Thebpatiphat et al.8 showed that manual keratometry was more accurate than automated keratometry in patients with keratoconus. Additionally, Hashemi et al.10 showed that there is increased error and unreliability with measurements of corneal power using optical biometry in eyes with keratoconus. Furthermore, the study also showed that Pentacam keratometry has better repeatability for corneal power measurements in this population compared to corneal topography or manual keratometry. However, in a separate study, Hashemi et al.3 compared calculating toric IOL powers using values from corneal topography, a Pentacam-derived refractive map, and Pentacam derived equivalent K readings in eyes with keratoconus. Comparing the SRK, SRK/II, and SRK/T formulas, the study concluded that the best method was to use corneal topography-derived keratometry with the SRK/T formula in mild cases of keratoconus and corneal topography-derived keratometry and manual keratometry with SRK/T and SRK/II in severe cases of keratoconus. Although these studies seem to suggest using Pentacam-derived measurements may improve IOL power calculation, there is currently no good way to incorporate this information with IOL power calculations for eyes with keratoconus, and Page 2 of 13
there also are no studies to our knowledge that have analyzed IOL power predictions based on Pentacam keratometry values versus optical biometry. The purpose of this study is to assess the predictive accuracy of various IOL power formulas in eyes with keratoconus. Currently, there is no consensus for the one best formula in these eyes. Furthermore, this study aims to examine how using Pentacam data might impact refractive outcomes in this population of eyes. Methods A retrospective chart review of eyes with keratoconus that underwent uncomplicated cataract surgery at the Wilmer Eye Institute at Johns Hopkins Hospital, Baltimore, Maryland, USA, and associated satellite practice locations between 2014 and 2018 was conducted. Potential study patients were identified through billing records of patients undergoing cataract surgery who were also at some point billed for a diagnosis of keratoconus. The diagnosis of keratoconus was confirmed for all eyes using topography information. Patients who had a postoperative best-corrected spectacle visual acuity (BSCVA) of worse than 20/40, a multifocal lens, a prior history of corneal surgeries or intraocular surgeries, or a history of ocular trauma were excluded. Eyes that had a history of corneal crosslinking were included, but those which had prior refractive surgery including laser-assisted in-situ keratomileusis (LASIK) or photorefractive keratectomy (PRK) were excluded. Patients with intraoperative complications such as capsular rupture or the placement of an anterior chamber, sulcus, or sutured lens were also excluded. Biometry data prior to cataract surgery was performed using an IOLMaster 500 (software version 5.1; Carl Zeiss Meditec AG, Jena, Germany), IOLMaster 700 (software version 1.0; Carl Zeiss Meditec AG), or Lenstar 900 (HaagStreit AG, Köniz, Switzerland). Additionally, preoperative topography information was obtained using an OCULUS Pentacam (OCULUS Optikgeräte GmbH, Wetzlar, Germany). Information regarding the IOL model and power implanted and final manifest refraction (MRx) within 14 to 60 days after surgery were obtained. Approval for this study was granted by the Johns Hopkins Hospital Institutional Review Board (IRB), and all research was performed in accordance with the Declaration of Helsinki.11 Eyes were categorized into stages of severity determined according to criteria established by Krumeich et al.12 Stage I included eyes that had corneal powers of 48 D or lower. Stage II contained eyes with corneal power between 48.01 D and 53 D, inclusive. Stage III had eyes with corneal powers greater than 53 D. The stage IV category (eyes with central scarring and unmeasurable refraction) was excluded due to the requirement of postoperative BSCVA of 20/40 or better for the study. Intraocular lens powers were calculated using preoperative biometry information and the Hoffer Q, SRK/T, Holladay I, Holladay II, Haigis, and Barrett Universal II formulas. The error between the formula-predicted postoperative refraction and the actual postoperative refraction was calculated. The results for the Barrett Universal II formula were obtained from the online calculator provided by the Asia-Pacific Association of Cataract and Refractive Surgeons (APACRS) (https://www.apacrs.org/barrett_universal2/) using assumed posterior curvature data. The Holladay II formula was calculated using the Holladay IOL Consultant Software (version 2013; Bellaire, Texas, USA). Optimized constants from the User Group for Page 3 of 13
Laser Interference Biometery (ULIB) website (http://ocusoft.de/ulib/c1.htm) were used. The predicted error of each formula for every eye was calculated by subtracting the predicted refraction based on the IOL actually implanted in the eye from the actual postoperative refraction. For example, if for one eye the SRK/T formula predicted the expected postoperative refraction to be – 0.75 D, spherical equivalent (SE) for the given implanted IOL and the actual postoperative refraction was – 0.25 D SE, then the resulting predicted error would be + 0.50 D for this hypothetical eye. Thus, a positive predicted error in refraction correlates to a more hyperopic result than the predicted refraction, and a negative predicted error in refraction correlates to a more myopic result than the predicted refraction. The absolute errors also were calculated as well as the percentage of eyes that had a predicted refractive error of within ± 0.50 D, ± 0.75 D, and ± 1.00 D. This method was used to compare the predictions of various IOL power formulas. Statistical analysis was carried out using descriptive statistics in Excel 2016 (version 1902; Microsoft Corporation; Redmond, WA, USA). The Friedman test, a nonparametric ANOVA for paired data, was used to determine statistical significance between different formulas and was calculated using an RStudio (Version 1.1.383, RStudio, Inc., Boston, MA). Post-hoc analysis was performed using the Conover method further adjusted by the Holm Family-Wise Error Rate between each formula. Results A total of 101 eyes with keratoconus that underwent uncomplicated cataract surgery were identified. Twenty-eight eyes were excluded due to post-operative BSCVA worse than 20/40. Among these eyes excluded, 17 eyes could not be refracted to 20/40 or better and 11 eyes had known posterior segment disease that limited BSCVA. Thus, a total of 73 eyes with keratoconus were included in the analysis (Table 1). The mean age of the sample was 65.0 ± 11.0 years old, with a range from 31 to 84 years. There were 46 keratoconus stage I eyes, 22 stage II eyes, and 5 stage III eyes according to the Krumeich et al.12 classification system. The average axial length of the sample was 24.93 mm ± 1.51 mm; the average mean corneal power was 47.01 D ± 3.50 D, and the average anterior chamber depth (ACD) was 3.58 D ± 0.48 D. The average final MRx SE was – 0.54 D ± 1.27 D. There were 9 different IOL models used (19 MA50BM [Alcon Laboratories Inc., Fort Worth, Texas, USA], 8 MA60MA [Alcon Laboratories Inc.], 24 SA60AT [Alcon Laboratories, Inc.], 4 SA60WF [Alcon Laboratories Inc.], 14 SN60WF [Alcon Laboratories Inc.], 1 SN6AT [Alcon Laboratories Inc.], 1 Softec HD SN [Lenstec, St. Petersburg, Florida, USA], 1 ZCB00 [Abbott Medical Optics Inc., Santa Ana, California, USA], and 1 ZCT600 [Abbott Medical Optics Inc.]). All formulas resulted in a positive mean predicted error (Table 2), indicating a tendency toward a hyperopic error. Among stage I eyes, the predicted error ranged from 0.10 D to 0.65 D. The predicted error generally increased for stage II eyes, with errors ranging from 0.36 D to 1.70 D. Predicted error further increased in stage III eyes, which had errors above 1.90 D. The formula with the lowest mean predicted error among stage I eyes was the Haigis formula, with an average predicted error of 0.10 D. In stage II eyes, the SRK/T had the lowest error with an average predicted error of 0.36 D, and in stage III, the Haigis had the lowest error with an average predicted error of 1.90 D. The Page 4 of 13
Friedman test showed a significant difference among all six formulas within stage I eyes (p < 0.001), stage II eyes (p < 0.001), and stage III eyes (p < 0.001). Post-hoc analysis using the Conover method further adjusted by the Holm Family-Wise Error Rate showed the Haigis was statically different from all of the other formulas in stage I eyes (p < 0.05), the SRK/T was statistically different than all formulas other than the Holladay II in stage II eyes (p < 0.05), and the Haigis was statistically different from the Hoffer Q, Holladay I, and Holladay II formulas in stage III eyes (p < 0.05). The Barrett Universal II online calculator was unable to provide a value for stage III eyes due to the upper limits in the accepted input variables. The median absolute predicted error of each formula divided into each keratoconus stage is shown in Table 3. These errors were calculated by taking the absolute value of the predicted error. The Friedman test showed that there was a difference among all six formulas for all three stages (stage I, p < 0.05; stage II, p < 0.01; stage III, p < 0.01). The Barrett Universal II formula resulted in the lowest median absolute error in both stage I and II eyes. There was a median absolute error of 0.445 D for stage I eyes and a median absolute error of 0.445 D for stage II eyes. No results were able to be calculated by the Barrett Universal II calculator among stage III eyes, again due to the upper bounds for accepted input variables. Post-hoc analysis using the Conover method further adjusted by the Holm Family-Wise Error Rate showed that the Barrett Universal II formula was statistically different from the Hoffer Q, Haigis, and Holladay II formulas among stage I eyes (p < 0.05). The Barrett Universal II formula was also statistically different from the Hoffer Q, SRK/T, Haigis, and Holladay II formulas among stage II eyes (p < 0.05). For stage III eyes, the formula with the lowest median absolute error was the Haigis formula with an error of 1.181 D. Post-hoc analysis also showed that in stage III eyes, the Haigis formula was statistically different from the Hoffer Q, Holladay I, and Holladay II formulas (p < 0.05). The percentage of eyes where the predicted refractive outcome by each formula was within ± 0.50 D, ± 0.75 D, or ± 1.00 D of the actual post-operative MRx is displayed in Table 4. For eyes in stage I, the Barrett Universal II formula had the highest percentage of eyes within ± 0.50 D, ± 0.75 D, and ± 1.00 D (52%, 63%, and 76% respectively). The Barrett Universal II formula also had the highest percentage eyes within ± 0.50 D, ± 0.75D, and ± 1.00 D for eyes in stage II (50%, 55%, and 59% respectively). The Haigis formula predicted the highest percentage of eyes within ± 0.50 D, ± 0.75 D, and ± 1.00 D for eyes categorized as stage III (40%, 40%, and 40%, respectively). It was not possible to calculate the percentage of eyes within set thresholds for stage III eyes using the Barrett Universal II formula due to restrictions in the range of input variables accepted by the online calculator. In general, the formulas that predicted the highest number of eyes within each threshold boundary (± 0.50 D, ± 0.75 D, and ± 1.00 D) for each stage of keratoconus (Table 4) correlate to the same formulas which predict the lowest median absolute errors for each stage (Table 3). Figure 1 compares corneal power measured by the optical biometer to corneal power measured by Pentacam. The Pentacam measured a lower corneal power in 75.4% (46/61) eyes. A linear regression is displayed in the graph with good correlation (R2 = 0.968). There is a trend where corneal powers reported by biometers are higher than corneal powers reported by Pentacam. For every 1 unit of corneal power measured by Page 5 of 13
biometer, the Pentacam measured 0.855 units of corneal power. On average, Pentacam derived corneal powers were 0.371 D less than optical biometer derived corneal powers (paired T-test, p < 0.05). Discussion The calculation of IOL power in eyes with keratoconus is challenging and results in decreased predictive accuracy. Our results similarly indicate that there is significantly increased error for calculation of IOL power in eyes with keratoconus versus in normal eyes. In normal eyes, modern formulas typically predict refractive outcomes that are within ± 0.5 D of actual postoperative refractive outcomes in about 75% of eyes13-15; however, in our results, the best formula, the Barrett Universal II formula, only achieved a ± 0.5 D predictive accuracy in 52% of eyes with mild, stage I keratoconus, with most other formulas only achieving around 40% accuracy (Table 4). There was a trend where the percentage of eyes with a predicted error within ± 0.5 D further decreased with more severe stages of keratoconus. In eyes with stage II keratoconus, the Barrett Universal II formula managed to achieved a predicted error within ± 0.5 D in 50% of eyes, which is similar to the accuracy achieved in stage I eyes (52%). In general, other formulas did not have similar percentages of eyes with a predicted error within ± 0.5 D between stage I and stage II keratoconus. Most formulas had around 20% of eyes with a predicted error within ± 0.5 D in eyes with stage II keratoconus. In stage III keratoconus, formulas were highly inaccurate, with predicted errors ranging from 1.90 D to 4.38 D (Table 2). Our results suggest that overall, current IOL formulas are less accurate in eyes with keratoconus than normal eyes. This accuracy decreases with keratoconus severity and in advanced keratoconus, where preoperative mean corneal power is greater than 48 D, postoperative refractive outcomes are almost unpredictable by current IOL formulas. Beyond corneal power, other preoperative characteristics of eyes within our study sample were similar to the general population of normal eyes. The average age of patients who had surgery was 65.0 years old, similar to the average age at which normal-eye patients have surgery, around 60 to 70 years old15-17. Similarly, the mean ACD in this sample, 3.58 mm, was similar to the mean ACD of normal adult emmetropic eyes, 3 to 4 mm.18 The average axial length in this sample was 24.93 mm, which is also similar to the 22 to 25 mm average axial length in normal adult eyes.18 Savini et al.9 observed that axial length was relatively high in their sample of keratoconic eyes, with 34.1% of eyes having an axial length greater than 26.0 mm. This trend of high axial length was not present in our sample of eyes, and our sample only had 19 eyes (26.0 %) with axial lengths greater than 26.0 mm. All six formulas assessed in this study resulted in mean hyperopic predicted errors. This finding is similar to previous studies. Savini et al.9 found a mean hyperopic predicted error in the Barrett Universal II, Haigis, Holladay I, Hoffer Q, and SRK/T formulas, and Kamiya et al.19 found a mean hyperopic predicted error in the Haigis, Holladay I, Hoffer Q, and SRK/T formulas. The mean hyperopic error may be a result of overestimation of the corneal power by optical biometers. Our series showed that there was a trend where optical biometer-measured corneal powers were greater than Pentacam-measured corneal powers (Figure 1). An IOL chosen based on an erroneously high corneal power Page 6 of 13
will result in too low of an IOL power implanted and a postoperative hyperopic error. Perhaps by using a net index of refraction, as used by most optical biometers and the Gullstrand model,20 optical biometers do not adequately account for the influence of the negatively powered posterior cornea. Thus, it is possible that the mean hyperopic predicted errors made by the formulas in this study may be a result of optical biometers overestimating corneal power in eyes with keratoconus. The Pentacam is also able to calculate the total corneal refractive power (TCRP) through ray tracing. There are studies which suggest that in eyes with keratoconus, the Pentacam TCRP calculated by ray tracing is more accurate of true corneal power than corneal power derived the standard keratometric index and radius of anterior curvature.21 Additionally, when TCRP is used for IOL power calculations in eyes with keratoconus, there is a myopic shift that occurs.22 Even though TCRP may be appropriate for determination of the true refractive power of the cornea, purely substituting TCRP for corneal power would create an error in the determination of estimated lens position by some formulas in this study. Thus, further investigation into how to best incorporate Pentacam derived measurements into IOL power calculation is needed. Although all formulas had a mean hyperopic predicted error, the Barrett Universal II formula was the best formula for eyes with stage I or II keratoconus. In normal eyes, the Barrett Universal II formula has also been one of the most accurate formulas.14-16 The Barrett Universal II formula had the lowest median absolute error (Table 3) and the most percentage of eyes with a predicted error within ± 0.5 D in eyes with stage I and stage II keratoconus (Table 4). In these eyes, the Barrett Universal II formula was the only formula to have a median absolute predicted error lower than 0.5 D. The ± 0.5 D predicted error threshold is an important gauge to measure formula performance because most lenses come in half-diopter increments, and errors smaller than 0.5 D generally do not affect spectacle independence. Although the Barrett Universal II formula was superior in eyes with stage I and stage II keratoconus, the formula was not able to be used in all keratoconic eyes in this sample— specifically eyes with stage III keratoconus. This was due to the upper bound of 55 D imposed on corneal power inputs by the online APACRS calculator. Thus, of the five remaining formulas, the Haigis formula performed the best in keratoconus stage III eyes based on median absolute error and the percentage of eyes with a predicted error within ± 0.5 D. This formula was the only formula to predict postoperative refractions within ± 0.5 D for any of the keratoconus stage III eyes. This finding is limited by the small number of eyes of the entire sample (5/73) that fell under the criteria for stage III keratoconus because only a small number of stage III eyes met the study inclusion criteria of BSCVA of 20/40 or better and underwent cataract surgery during our study period. Furthermore, although the Haigis formula achieved predicted errors within ± 0.5 D for two (40 %) of these eyes, the interquartile range of the median absolute predicted error was large (3.51 D) (Table 3), and the actual predicted errors for these eyes ranged from – 0.59 D to + 4.38 D. Thus, there is still significant inaccuracy in IOL power prediction using the Haigis formula in eyes with stage III keratoconus. There was a discrepancy in which formulas had lowest predicted errors versus median absolute predicted errors. In eyes with stage I keratoconus, the Haigis had a lower mean predicted error (0.10 D) than the Barrett Universal II, which had a higher mean predicted error (0.39 D). However, the median absolute predicted error of the Haigis Page 7 of 13
formula (0.581 D) in eyes with stage I keratoconus was significantly higher than the median absolute predicted error by the Barrett Universal II formula (0.445 D). Similarly, in keratoconus stage II eyes, the SRK/T had a lower mean predicted error (0.36 D) than the Barrett Universal II formula (0.95 D) but had a higher median absolute predicted error (0.991 D) than the Barrett Universal II formula (0.445 D). Both these findings stem from the Haigis and SRK/T formulas having positive and negative predicted errors which were higher in magnitude than the Barrett Universal II formula. These predicted errors that straddle zero negate one another when calculating predicted error, resulting in a predicted error closer to zero, but an increased median absolute predicted error. Thus, although the Haigis and SRK/T formulas seem to perform better based on mean predicted error, the Barrett Universal II formula results in errors that are lower in magnitude and is the superior formula in stage I and stage II keratoconic eyes. To our knowledge, there have not been previous studies that have showed that the Barrett Universal II formula provides the lowest predicted error and highest percentage of eyes with a predicted error within ± 0.5 D. Savini et al.9 found that the SRK/T formula was superior to the Barrett Universal II formula based on both these measures. One possible source of this difference may stem from differences in characteristics between the sample of eyes in their study and in this study that influence which formula performs better. In the study by Savini et al.,9 34.1% of eyes had axial lengths longer than 26.0 mm; however, only 26.0% of our study sample had eyes with axial lengths longer than 26.0 mm. In eyes with long axial lengths, the SRK/T formula has been demonstrated as one of the most accurate formulas by Hoffer,23 and this may contribute to the reason why Savini et al.9 found that the SRK/T formula performed best in their study, while our results showed that the Barrett Universal II formula performed best. Although there are studies prior to Savini et al.9 that also have concluded that the SRK/T formula was the most accurate formula for eyes with keratoconus,2,3 these other studies did not include the Barrett Universal II formula among the formulas they assessed. Kamiya et al.2 concluded that the SRK/T formula was better than the Haigis, Hoffer Q, and Holladay I formulas; Hashemi et al.3 found that the SRK/T formula was better than the Hoffer Q and Holladay I formulas. In all three of these studies,2,3,9 there was a trend of decreasing formula accuracy with increasing keratoconus severity, and this finding is also reflected in our results. Other studies have found that IOL formulas in general do not perform well in eyes with keratoconus. Savini et al.9 found that the percentage of eyes with a predicted error within ± 1.0 D was between 43.90% to 60.98% depending on the formula used. Similarly, Leccisotti5 showed that in eyes where IOL powers were calculated using the Holladay II formula, only 47% had a defocus equivalent within ± 1.0 D one year after surgery. Watson et al.7 reported that 60% of eyes with stage I keratoconus with an IOL power calculated using the SRK/T formula, had a predicted error within ± 1.0 D. These figures are similar to our series, which had predicted errors within ± 1.0 D in 57% to 66% of eyes depending on the formula used. Compared to normal eyes, this level of accuracy is considerably lower, with a study by Melles et al.15 showing 95.0% to 97.8% of eyes achieving predicted error within ± 1.0 D and 69.6% to 80.8% of eyes having a predicted error within ± 0.5 D depending on the formula used. With the current formulas, IOL power calculation in eyes with keratoconus still remains inaccurate relative to IOL power calculation in normal eyes. Page 8 of 13
One limitation of this study is its retrospective nature. The study was performed across multiple satellite locations, each of which used different optical biometers, and surgery was performed by different surgeons. There also were multiple IOL models implanted. These limitations prevented optimization of formula constants. Instead, constants published on the ULIB website were used, which is more in line with real clinical scenarios but not best practice for the purpose of comparing formula accuracy.24 Additionally, we did not exclude eyes that had a previous history of crosslinking; thus, having both eyes that had undergone the crosslinking procedure and eyes that had not may confound the results. Eyes that had intracorneal rings were excluded from this study; thus, these results are not able to be applied to keratoconic eyes with intracorneal rings. Eyes that had a previous history of keratomileusis, such as LASIK or PRK, were also excluded, so these results are also not able to be generalized to postlaser surgery corneal ectasia. The results of this study are also constrained to eyes with post-operative BSCVA of 20/40 or better. Keratoconus can cause significant impact on visual acuity resulting in BSCVA worse than 20/40, and these eyes may have a greater post-operative refractive error. Thus, IOL power formula errors may actually be worse when considering the overall population of keratoconic eyes which undergo cataract surgery. Finally, this series had a small sample size of eyes with stage III keratoconus, which limits the power of this study within the keratoconus stage III population. In summary, our results show that the Barrett Universal II formula performed best in the eyes in which it can be applied. All formulas had a tendency toward hyperopic errors, which may result from overestimation of corneal power by optical biometers. Generally, patients tolerate myopic errors better than hyperopic errors; thus, clinicians should take into consideration that current formulas tend to result in hyperopic errors in eyes with keratoconus. It is important to manage patient expectations in increasingly severe stages of keratoconus because predicted error increases significantly with more advanced keratoconus. Given that only 39% to 52% of eyes with mild keratoconus achieve a predicted error within ± 0.5 D depending on the formula used, managing expectations of spectacle independence is also important. Overall, there is room to improve current formulas to better predict IOL powers in eyes with keratoconus, and future research is required to develop a single formula that performs best across the spectrum of keratoconus severity.
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Acknowledgements and Disclosures: a. The authors would like to acknowledge financial support from the Sandra and Larry Small Fund and acknowledge support for the statistical analysis from the National Center for Research Resources and the National Center for Advancing Translational Sciences (NCATS) of the National Institutes of Health through Grant Number 1UL1TR001079. b. Dr. Divya Srikumaran is a consultant for Alcon Laboratories, Inc. Dr. John Ladas is a president at Advanced Euclidean Solutions. All other authors have no financial disclosures. c. No other acknowledgements.
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References 1. Kovacs I, Mihaltz K, Nemeth J, Nagy ZZ. Anterior chamber characteristics of keratoconus assessed by rotating scheimpflug imaging. J Cataract Refract Surg. 2010;36(7):1101-1106. 2. Kamiya K, Shimizu K, Miyake T. Changes in astigmatism and corneal higher-order aberrations after phacoemulsification with toric intraocular lens implantation for mild keratoconus with cataract. Jpn J Ophthalmol. 2016;60(4):302-308. 3. Hashemi H, Heidarian S, Seyedian MA, Yekta A, Khabazkhoob M. Evaluation of the results of using toric IOL in the cataract surgery of keratoconus patients. Eye Contact Lens. 2015;41(6):354-358 4. Tamaoki A, Kojima T, Hasegawa A, Nakamura H, Tanaka K, Ichikawa K. Intraocular lens power calculation in cases with posterior keratoconus. J Cataract Refract Surg. 2015;41(10):2190-2195. 5. Leccisotti A. Refractive lens exchange in keratoconus. J Cataract Refract Surg. 2006;32(5):742-746. 6. Alio JL, Pena-Garcia P, Abdulla Guliyeva F, Soria FA, Zein G, Abu-Mustafa SK. MICS with toric intraocular lenses in keratoconus: Outcomes and predictability analysis of postoperative refraction. Br J Ophthalmol. 2014;98(3):365-370. 7. Watson MP, Anand S, Bhogal M, et al. Cataract surgery outcome in eyes with keratoconus. Br J Ophthalmol. 2014;98(3):361-364. 8. Thebpatiphat N, Hammersmith KM, Rapuano CJ, Ayres BD, Cohen EJ. Cataract surgery in keratoconus. Eye Contact Lens. 2007;33(5):244-246. 9. Savini G, Abbate R, Hoffer KJ, et al. Intraocular lens power calculation in eyes with keratoconus. J Cataract Refract Surg. 2019;45(5):576-581. 10. Hashemi H, Yekta A, Khabazkhoob M. Effect of keratoconus grades on repeatability of keratometry readings: Comparison of 5 devices. J Cataract Refract Surg. 2015;41(5):1065-1072. 11. World Medical Association. World medical association declaration of helsinki: Ethical principles for medical research involving human subjects. JAMA. 2013;310(20):2191-2194. 12. Krumeich JH, Daniel J, Knulle A. Live-epikeratophakia for keratoconus. J Cataract Refract Surg. 1998;24(4):456-463.
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13. Kane JX, Van Heerden A, Atik A, Petsoglou C. Intraocular lens power formula accuracy: Comparison of 7 formulas. J Cataract Refract Surg. 2016;42(10):1490-1500. 14. Cooke DL, Cooke TL. Comparison of 9 intraocular lens power calculation formulas. J Cataract Refract Surg. 2016;42(8):1157-1164. 15. Melles RB, Holladay JT, Chang WJ. Accuracy of intraocular lens calculation formulas. Ophthalmology. 2018;125(2):169-178. 16. Kauh CY, Blachley TS, Lichter PR, Lee PP, Stein JD. Geographic variation in the rate and timing of cataract surgery among US communities. JAMA Ophthalmol. 2016;134(3):267-276. 17. Kansal V, Schlenker M, Ahmed IIK. Interocular axial length and corneal power differences as predictors of postoperative refractive outcomes after cataract surgery. Ophthalmology. 2018;125(7):972-981. 18. Bhardwaj V, Rajeshbhai GP. Axial length, anterior chamber depth-a study in different age groups and refractive errors. J Clin Diagn Res. 2013;7(10):2211-2212. 19. Kamiya K, Iijima K, Nobuyuki S, et al. Predictability of intraocular lens power calculation for cataract with keratoconus: A multicenter study. Sci Rep. 2018;8(1):131-w. 20. Gullstrand A. Appendices II and IV. Helmholtz’s Handbuch der Physiologischen Optik. 1909;1:30-415. 21. Kamiya K, Kono Y, Takahashi M, Shoji N. Comparison of simulated keratometry and total refractive power for keratoconus according to the stage of amsler-krumeich classification. Sci Rep. 2018;8(1):1243-1. 22. Kamiya K, Iijima K, Nobuyuki S, et al. Predictability of intraocular lens power calculation for cataract with keratoconus: A multicenter study. Sci Rep. 2018;8(1):131-w. 23. Hoffer KJ. The hoffer Q formula: A comparison of theoretic and regression formulas. Journal of Cataract and Refractive Surgery. 1993;19(6):700-712. 24. Hoffer KJ, Aramberri J, Haigis W, et al. Protocols for studies of intraocular lens formula accuracy. Am J Ophthalmol. 2015;160(3):40-405.e1.
Page 12 of 13
Captions Figure 1. Corneal power measured by optical biometers compared to corneal power measured by Pentacam.
Page 13 of 13
Table 1. Patient demographics by keratoconus stage. Stage I (Km ≤ 48D)
Stage II (48D < Km ≤ 53D)
Stage III (Km > 53D)
Total
46
22
5
73
Mean age [range] (years)
64.8 [31 – 84]
65.1 [44 – 79]
66.4 [63 – 73]
65.0 [31 – 84]
Mean AL (mm) ± SD
25.00 ± 1.24
24.66 ± 2.01
25.46 ± 1.22
24.93 ± 1.51
Mean Km (D) ± SD
44.98 ± 1.50
49.15 ± 1.14
56.34 ± 2.68
47.01 ± 3.50
Mean ACD (mm) ± SD
3.58 ± 0.45
3.57 ± 0.54
3.64 ± 0.61
3.58 ± 0.48
Number of eyes (n)
ACD = anterior chamber depth; AL = axial length; Km = mean corneal power
Table 2. Mean refractive predicted error by formula and keratoconus stage. The formula with the lowest predicted error for each stage is bolded. *, †, and ‡, indicate a statistical difference (p<0.05) from the formula with the lowest predicted error (in bold) in each stage determined by post-hoc analysis with the Conover method further adjusted by the Holm Family-Wise Error Rate.
Mean ± 95% CI [95% CI] Stage I (Km ≤ 48D)
Stage II (48D < Km ≤ 53D)
Hoffer Q
0.65* [0.38 – 0.92]
1.70 [0.78 – 2.62]
4.00 [2.46 – 5.55]
SRK/T
0.12* [-0.15 – 0.40]
0.36 [-0.48 – 1.21]
2.51 [0.88 – 4.14]
†
†
Stage III (Km > 53D) ‡
‡
Holladay I
0.38* [0.11 – 0.65]
1.21 [0.34 – 2.08]
2.99 [1.19 – 4.80]
Haigis
0.10 [-0.22 – 0.42]
1.12† [0.32 – 2.08]
1.90 [-0.59 – 4.38]
†
#
Barrett
0.39* [0.10 – 0.69]
0.95 [0.10 – 1.80]
Not available
Holladay II
0.56* [0.28 – 0.84]
1.49 [0.61 – 1.37]
4.38 [2.56 – 6.20]
Km = mean corneal power
‡
Table 3. Median absolute predicted error by formula and keratoconus stage. The formula with the lowest predicted error for each stage is bolded. *, †, and ‡, indicate a statistical difference (p<0.05) from the formula with the lowest predicted error (in bold) in each stage determined by post-hoc analysis with the Conover method further adjusted by the Holm Family-Wise Error Rate.
Hoffer Q
Median Absolute Error (D) [Interquartile Range] Stage I Stage II Stage III (Km ≤ 48D) (48D < Km ≤ 53D) (Km > 53D) † ‡ 0.573* [0.844] 1.009 [1.897] 4.217 [0.855] †
SRK/T
0.615 [0.807]
0.991 [0.650]
1.741 [1.734]
Holladay I
0.645 [0.780]
1.002 [1.816]
1.962 [2.504]
Haigis
0.581* [0.979]
1.448 [1.226]
1.181 [3.511]
Barrett
0.445 [0.764]
0.445 [1.72]
Not available
Holladay II 0.580* [0.909] Km = mean corneal power
†
†
1.190 [1.931]
‡
‡
#
4.520 [0.720]
Table 4. Percent of eyes within predicted error ranges. Error within ± 0.50 D (%)
Hoffer Q SRK/T Holladay I Haigis Barrett Holladay II
Error within ± 0.75 D (%)
Error within ± 1.00 D (%)
Stage I
Stage II
Stage III
Stage I
Stage II
Stage III
Stage I
Stage II
Stage III
41 48 39 39 52
18 18 41 23 50
0 0 0 40
61 61 61 61 63
27 36 45 27 55
0 0 0 40
67 72 74 70 76
50 50 50 36 59
0 0 0 40
39
23
57
32
73
46
n/a = not available
n/a 0
n/a 0
n/a 0
Corneal Power Measured by Pentacam versus Optical Biometer Pentacam Measured Mean Corneal Power (D)
60
55
y = 0.855x + 6.4333 50 R² = 0.968
45
40
35 35
40
45
50
55
Optical Biometer Measured Mean Corneal Power (D)
60
65
Kendrick Wang is a medical student at Johns Hopkins University School of Medicine. He is on the path to becoming an ophthalmologist, and his current research interests include cataract surgery and resident education policies. He has a bachelor of science degree in Bioengineering from Stanford University. His previous research includes work done at NASA Ames Research Center in the origins of life and the application of synthetic biology to space travel.
S0002-9394(19)30576-8
DOI:
https://doi.org/10.1016/j.ajo.2019.11.019
Reference:
AJOPHT 11148
To appear in:
American Journal of Ophthalmology
Received Date: 12 August 2019 Revised Date:
11 November 2019
Accepted Date: 14 November 2019
Please cite this article as: Wang KM, Jun AS, Ladas JG, Siddiqui AA, Woreta F, Srikumaran D, Accuracy of intraocular lens formulas in eyes with keratoconus, American Journal of Ophthalmology (2019), doi: https://doi.org/10.1016/j.ajo.2019.11.019. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Elsevier Inc. All rights reserved.
Accuracy of intraocular lens formulas in eyes with keratoconus Short title: Accuracy of IOL formulas in eyes with keratoconus. Kendrick M Wang1, Albert S Jun1, John G Ladas1,2, Aazim A Siddiqui3, Fasika Woreta1, Divya Srikumaran1 1
Wilmer Eye Institute, Johns Hopkins University School of Medicine, 600 North Wolfe Street, Baltimore, MD 21287
2
Maryland Eye Consultants and Surgeons, 2101 Medical Park Drive, Suite 101, Silver Spring, MD 20902
3
Department of Ophthalmology and Visual Sciences, Montefiore Medical Center, Albert Einstein College of Medicine, 3332 Rochambeau Avenue, 3rd floor, Room 306, Bronx, NY 10467
Corresponding Author: Divya Srikumaran MD, Wilmer Eye Institute at Odenton, 1106 Annapolis Road, Suite 290, Odenton, MD 21113. Phone: (410) 874-1428. Email: [email protected]
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Introduction Keratoconus is a progressive non-inflammatory condition of the cornea characterized by corneal ectasia and thinning as well as the development of high irregular astigmatism. Patients with mild to moderate disease may achieve adequate visual acuity with spectacle correction, whereas those with advanced disease typically require contacts lenses. Calculation of intraocular lenses (IOLs) in patients with keratoconus can be challenging for a number of reasons, including the corneal abnormalities and deeper anterior chambers1 seen in these patients. Changes to the cornea typically include inferior steepening and apex thinning; however, steepening and thinning can occur throughout the cornea. Corneal changes in keratoconus influence the ratio between the anterior corneal curvature and posterior corneal curvature. This challenges the assumption that the Gullstrand schematic eye model is an appropriate model for the derivation of the standard keratometric index of refraction used by keratometers and corneal topographers. There is limited literature on the calculation of IOL power in eyes with keratoconus.2-8 All studies show that there tends to be a hyperopic error in IOL formulas that increases as keratoconus worsens.2,7-9 There also is a dearth of literature on which formula results in the most accurate IOL power prediction. Although some literature concludes that the SRK/T is the most accurate formula,3,6,9 other studies have recommended using the SRK/II formula in keratoconic eyes.3,8 Furthermore, there is a growing interest in using toric IOLs to treat astigmatism from keratoconus.2,3,6 Additionally, improving accuracy of IOL power predictions is especially needed in eyes that are preoperatively spectaclecorrected versus preoperatively contact-lens corrected. Eyes with keratoconus tend to be longer than normal eyes, with longer axial lengths and deeper anterior chamber depths.1 This affects the estimated lens position (ELP) and contributes to inaccuracy in prediction of IOL power. Optical biometry in patients with keratoconus is also a source of error for IOL power predictions. Watson et al.7 showed that optical biometry tends to overestimate corneal power, resulting in hyperopic outcomes due to inadequate power in the IOL implanted. Thebpatiphat et al.8 showed that manual keratometry was more accurate than automated keratometry in patients with keratoconus. Additionally, Hashemi et al.10 showed that there is increased error and unreliability with measurements of corneal power using optical biometry in eyes with keratoconus. Furthermore, the study also showed that Pentacam keratometry has better repeatability for corneal power measurements in this population compared to corneal topography or manual keratometry. However, in a separate study, Hashemi et al.3 compared calculating toric IOL powers using values from corneal topography, a Pentacam-derived refractive map, and Pentacam derived equivalent K readings in eyes with keratoconus. Comparing the SRK, SRK/II, and SRK/T formulas, the study concluded that the best method was to use corneal topography-derived keratometry with the SRK/T formula in mild cases of keratoconus and corneal topography-derived keratometry and manual keratometry with SRK/T and SRK/II in severe cases of keratoconus. Although these studies seem to suggest using Pentacam-derived measurements may improve IOL power calculation, there is currently no good way to incorporate this information with IOL power calculations for eyes with keratoconus, and Page 2 of 13
there also are no studies to our knowledge that have analyzed IOL power predictions based on Pentacam keratometry values versus optical biometry. The purpose of this study is to assess the predictive accuracy of various IOL power formulas in eyes with keratoconus. Currently, there is no consensus for the one best formula in these eyes. Furthermore, this study aims to examine how using Pentacam data might impact refractive outcomes in this population of eyes. Methods A retrospective chart review of eyes with keratoconus that underwent uncomplicated cataract surgery at the Wilmer Eye Institute at Johns Hopkins Hospital, Baltimore, Maryland, USA, and associated satellite practice locations between 2014 and 2018 was conducted. Potential study patients were identified through billing records of patients undergoing cataract surgery who were also at some point billed for a diagnosis of keratoconus. The diagnosis of keratoconus was confirmed for all eyes using topography information. Patients who had a postoperative best-corrected spectacle visual acuity (BSCVA) of worse than 20/40, a multifocal lens, a prior history of corneal surgeries or intraocular surgeries, or a history of ocular trauma were excluded. Eyes that had a history of corneal crosslinking were included, but those which had prior refractive surgery including laser-assisted in-situ keratomileusis (LASIK) or photorefractive keratectomy (PRK) were excluded. Patients with intraoperative complications such as capsular rupture or the placement of an anterior chamber, sulcus, or sutured lens were also excluded. Biometry data prior to cataract surgery was performed using an IOLMaster 500 (software version 5.1; Carl Zeiss Meditec AG, Jena, Germany), IOLMaster 700 (software version 1.0; Carl Zeiss Meditec AG), or Lenstar 900 (HaagStreit AG, Köniz, Switzerland). Additionally, preoperative topography information was obtained using an OCULUS Pentacam (OCULUS Optikgeräte GmbH, Wetzlar, Germany). Information regarding the IOL model and power implanted and final manifest refraction (MRx) within 14 to 60 days after surgery were obtained. Approval for this study was granted by the Johns Hopkins Hospital Institutional Review Board (IRB), and all research was performed in accordance with the Declaration of Helsinki.11 Eyes were categorized into stages of severity determined according to criteria established by Krumeich et al.12 Stage I included eyes that had corneal powers of 48 D or lower. Stage II contained eyes with corneal power between 48.01 D and 53 D, inclusive. Stage III had eyes with corneal powers greater than 53 D. The stage IV category (eyes with central scarring and unmeasurable refraction) was excluded due to the requirement of postoperative BSCVA of 20/40 or better for the study. Intraocular lens powers were calculated using preoperative biometry information and the Hoffer Q, SRK/T, Holladay I, Holladay II, Haigis, and Barrett Universal II formulas. The error between the formula-predicted postoperative refraction and the actual postoperative refraction was calculated. The results for the Barrett Universal II formula were obtained from the online calculator provided by the Asia-Pacific Association of Cataract and Refractive Surgeons (APACRS) (https://www.apacrs.org/barrett_universal2/) using assumed posterior curvature data. The Holladay II formula was calculated using the Holladay IOL Consultant Software (version 2013; Bellaire, Texas, USA). Optimized constants from the User Group for Page 3 of 13
Laser Interference Biometery (ULIB) website (http://ocusoft.de/ulib/c1.htm) were used. The predicted error of each formula for every eye was calculated by subtracting the predicted refraction based on the IOL actually implanted in the eye from the actual postoperative refraction. For example, if for one eye the SRK/T formula predicted the expected postoperative refraction to be – 0.75 D, spherical equivalent (SE) for the given implanted IOL and the actual postoperative refraction was – 0.25 D SE, then the resulting predicted error would be + 0.50 D for this hypothetical eye. Thus, a positive predicted error in refraction correlates to a more hyperopic result than the predicted refraction, and a negative predicted error in refraction correlates to a more myopic result than the predicted refraction. The absolute errors also were calculated as well as the percentage of eyes that had a predicted refractive error of within ± 0.50 D, ± 0.75 D, and ± 1.00 D. This method was used to compare the predictions of various IOL power formulas. Statistical analysis was carried out using descriptive statistics in Excel 2016 (version 1902; Microsoft Corporation; Redmond, WA, USA). The Friedman test, a nonparametric ANOVA for paired data, was used to determine statistical significance between different formulas and was calculated using an RStudio (Version 1.1.383, RStudio, Inc., Boston, MA). Post-hoc analysis was performed using the Conover method further adjusted by the Holm Family-Wise Error Rate between each formula. Results A total of 101 eyes with keratoconus that underwent uncomplicated cataract surgery were identified. Twenty-eight eyes were excluded due to post-operative BSCVA worse than 20/40. Among these eyes excluded, 17 eyes could not be refracted to 20/40 or better and 11 eyes had known posterior segment disease that limited BSCVA. Thus, a total of 73 eyes with keratoconus were included in the analysis (Table 1). The mean age of the sample was 65.0 ± 11.0 years old, with a range from 31 to 84 years. There were 46 keratoconus stage I eyes, 22 stage II eyes, and 5 stage III eyes according to the Krumeich et al.12 classification system. The average axial length of the sample was 24.93 mm ± 1.51 mm; the average mean corneal power was 47.01 D ± 3.50 D, and the average anterior chamber depth (ACD) was 3.58 D ± 0.48 D. The average final MRx SE was – 0.54 D ± 1.27 D. There were 9 different IOL models used (19 MA50BM [Alcon Laboratories Inc., Fort Worth, Texas, USA], 8 MA60MA [Alcon Laboratories Inc.], 24 SA60AT [Alcon Laboratories, Inc.], 4 SA60WF [Alcon Laboratories Inc.], 14 SN60WF [Alcon Laboratories Inc.], 1 SN6AT [Alcon Laboratories Inc.], 1 Softec HD SN [Lenstec, St. Petersburg, Florida, USA], 1 ZCB00 [Abbott Medical Optics Inc., Santa Ana, California, USA], and 1 ZCT600 [Abbott Medical Optics Inc.]). All formulas resulted in a positive mean predicted error (Table 2), indicating a tendency toward a hyperopic error. Among stage I eyes, the predicted error ranged from 0.10 D to 0.65 D. The predicted error generally increased for stage II eyes, with errors ranging from 0.36 D to 1.70 D. Predicted error further increased in stage III eyes, which had errors above 1.90 D. The formula with the lowest mean predicted error among stage I eyes was the Haigis formula, with an average predicted error of 0.10 D. In stage II eyes, the SRK/T had the lowest error with an average predicted error of 0.36 D, and in stage III, the Haigis had the lowest error with an average predicted error of 1.90 D. The Page 4 of 13
Friedman test showed a significant difference among all six formulas within stage I eyes (p < 0.001), stage II eyes (p < 0.001), and stage III eyes (p < 0.001). Post-hoc analysis using the Conover method further adjusted by the Holm Family-Wise Error Rate showed the Haigis was statically different from all of the other formulas in stage I eyes (p < 0.05), the SRK/T was statistically different than all formulas other than the Holladay II in stage II eyes (p < 0.05), and the Haigis was statistically different from the Hoffer Q, Holladay I, and Holladay II formulas in stage III eyes (p < 0.05). The Barrett Universal II online calculator was unable to provide a value for stage III eyes due to the upper limits in the accepted input variables. The median absolute predicted error of each formula divided into each keratoconus stage is shown in Table 3. These errors were calculated by taking the absolute value of the predicted error. The Friedman test showed that there was a difference among all six formulas for all three stages (stage I, p < 0.05; stage II, p < 0.01; stage III, p < 0.01). The Barrett Universal II formula resulted in the lowest median absolute error in both stage I and II eyes. There was a median absolute error of 0.445 D for stage I eyes and a median absolute error of 0.445 D for stage II eyes. No results were able to be calculated by the Barrett Universal II calculator among stage III eyes, again due to the upper bounds for accepted input variables. Post-hoc analysis using the Conover method further adjusted by the Holm Family-Wise Error Rate showed that the Barrett Universal II formula was statistically different from the Hoffer Q, Haigis, and Holladay II formulas among stage I eyes (p < 0.05). The Barrett Universal II formula was also statistically different from the Hoffer Q, SRK/T, Haigis, and Holladay II formulas among stage II eyes (p < 0.05). For stage III eyes, the formula with the lowest median absolute error was the Haigis formula with an error of 1.181 D. Post-hoc analysis also showed that in stage III eyes, the Haigis formula was statistically different from the Hoffer Q, Holladay I, and Holladay II formulas (p < 0.05). The percentage of eyes where the predicted refractive outcome by each formula was within ± 0.50 D, ± 0.75 D, or ± 1.00 D of the actual post-operative MRx is displayed in Table 4. For eyes in stage I, the Barrett Universal II formula had the highest percentage of eyes within ± 0.50 D, ± 0.75 D, and ± 1.00 D (52%, 63%, and 76% respectively). The Barrett Universal II formula also had the highest percentage eyes within ± 0.50 D, ± 0.75D, and ± 1.00 D for eyes in stage II (50%, 55%, and 59% respectively). The Haigis formula predicted the highest percentage of eyes within ± 0.50 D, ± 0.75 D, and ± 1.00 D for eyes categorized as stage III (40%, 40%, and 40%, respectively). It was not possible to calculate the percentage of eyes within set thresholds for stage III eyes using the Barrett Universal II formula due to restrictions in the range of input variables accepted by the online calculator. In general, the formulas that predicted the highest number of eyes within each threshold boundary (± 0.50 D, ± 0.75 D, and ± 1.00 D) for each stage of keratoconus (Table 4) correlate to the same formulas which predict the lowest median absolute errors for each stage (Table 3). Figure 1 compares corneal power measured by the optical biometer to corneal power measured by Pentacam. The Pentacam measured a lower corneal power in 75.4% (46/61) eyes. A linear regression is displayed in the graph with good correlation (R2 = 0.968). There is a trend where corneal powers reported by biometers are higher than corneal powers reported by Pentacam. For every 1 unit of corneal power measured by Page 5 of 13
biometer, the Pentacam measured 0.855 units of corneal power. On average, Pentacam derived corneal powers were 0.371 D less than optical biometer derived corneal powers (paired T-test, p < 0.05). Discussion The calculation of IOL power in eyes with keratoconus is challenging and results in decreased predictive accuracy. Our results similarly indicate that there is significantly increased error for calculation of IOL power in eyes with keratoconus versus in normal eyes. In normal eyes, modern formulas typically predict refractive outcomes that are within ± 0.5 D of actual postoperative refractive outcomes in about 75% of eyes13-15; however, in our results, the best formula, the Barrett Universal II formula, only achieved a ± 0.5 D predictive accuracy in 52% of eyes with mild, stage I keratoconus, with most other formulas only achieving around 40% accuracy (Table 4). There was a trend where the percentage of eyes with a predicted error within ± 0.5 D further decreased with more severe stages of keratoconus. In eyes with stage II keratoconus, the Barrett Universal II formula managed to achieved a predicted error within ± 0.5 D in 50% of eyes, which is similar to the accuracy achieved in stage I eyes (52%). In general, other formulas did not have similar percentages of eyes with a predicted error within ± 0.5 D between stage I and stage II keratoconus. Most formulas had around 20% of eyes with a predicted error within ± 0.5 D in eyes with stage II keratoconus. In stage III keratoconus, formulas were highly inaccurate, with predicted errors ranging from 1.90 D to 4.38 D (Table 2). Our results suggest that overall, current IOL formulas are less accurate in eyes with keratoconus than normal eyes. This accuracy decreases with keratoconus severity and in advanced keratoconus, where preoperative mean corneal power is greater than 48 D, postoperative refractive outcomes are almost unpredictable by current IOL formulas. Beyond corneal power, other preoperative characteristics of eyes within our study sample were similar to the general population of normal eyes. The average age of patients who had surgery was 65.0 years old, similar to the average age at which normal-eye patients have surgery, around 60 to 70 years old15-17. Similarly, the mean ACD in this sample, 3.58 mm, was similar to the mean ACD of normal adult emmetropic eyes, 3 to 4 mm.18 The average axial length in this sample was 24.93 mm, which is also similar to the 22 to 25 mm average axial length in normal adult eyes.18 Savini et al.9 observed that axial length was relatively high in their sample of keratoconic eyes, with 34.1% of eyes having an axial length greater than 26.0 mm. This trend of high axial length was not present in our sample of eyes, and our sample only had 19 eyes (26.0 %) with axial lengths greater than 26.0 mm. All six formulas assessed in this study resulted in mean hyperopic predicted errors. This finding is similar to previous studies. Savini et al.9 found a mean hyperopic predicted error in the Barrett Universal II, Haigis, Holladay I, Hoffer Q, and SRK/T formulas, and Kamiya et al.19 found a mean hyperopic predicted error in the Haigis, Holladay I, Hoffer Q, and SRK/T formulas. The mean hyperopic error may be a result of overestimation of the corneal power by optical biometers. Our series showed that there was a trend where optical biometer-measured corneal powers were greater than Pentacam-measured corneal powers (Figure 1). An IOL chosen based on an erroneously high corneal power Page 6 of 13
will result in too low of an IOL power implanted and a postoperative hyperopic error. Perhaps by using a net index of refraction, as used by most optical biometers and the Gullstrand model,20 optical biometers do not adequately account for the influence of the negatively powered posterior cornea. Thus, it is possible that the mean hyperopic predicted errors made by the formulas in this study may be a result of optical biometers overestimating corneal power in eyes with keratoconus. The Pentacam is also able to calculate the total corneal refractive power (TCRP) through ray tracing. There are studies which suggest that in eyes with keratoconus, the Pentacam TCRP calculated by ray tracing is more accurate of true corneal power than corneal power derived the standard keratometric index and radius of anterior curvature.21 Additionally, when TCRP is used for IOL power calculations in eyes with keratoconus, there is a myopic shift that occurs.22 Even though TCRP may be appropriate for determination of the true refractive power of the cornea, purely substituting TCRP for corneal power would create an error in the determination of estimated lens position by some formulas in this study. Thus, further investigation into how to best incorporate Pentacam derived measurements into IOL power calculation is needed. Although all formulas had a mean hyperopic predicted error, the Barrett Universal II formula was the best formula for eyes with stage I or II keratoconus. In normal eyes, the Barrett Universal II formula has also been one of the most accurate formulas.14-16 The Barrett Universal II formula had the lowest median absolute error (Table 3) and the most percentage of eyes with a predicted error within ± 0.5 D in eyes with stage I and stage II keratoconus (Table 4). In these eyes, the Barrett Universal II formula was the only formula to have a median absolute predicted error lower than 0.5 D. The ± 0.5 D predicted error threshold is an important gauge to measure formula performance because most lenses come in half-diopter increments, and errors smaller than 0.5 D generally do not affect spectacle independence. Although the Barrett Universal II formula was superior in eyes with stage I and stage II keratoconus, the formula was not able to be used in all keratoconic eyes in this sample— specifically eyes with stage III keratoconus. This was due to the upper bound of 55 D imposed on corneal power inputs by the online APACRS calculator. Thus, of the five remaining formulas, the Haigis formula performed the best in keratoconus stage III eyes based on median absolute error and the percentage of eyes with a predicted error within ± 0.5 D. This formula was the only formula to predict postoperative refractions within ± 0.5 D for any of the keratoconus stage III eyes. This finding is limited by the small number of eyes of the entire sample (5/73) that fell under the criteria for stage III keratoconus because only a small number of stage III eyes met the study inclusion criteria of BSCVA of 20/40 or better and underwent cataract surgery during our study period. Furthermore, although the Haigis formula achieved predicted errors within ± 0.5 D for two (40 %) of these eyes, the interquartile range of the median absolute predicted error was large (3.51 D) (Table 3), and the actual predicted errors for these eyes ranged from – 0.59 D to + 4.38 D. Thus, there is still significant inaccuracy in IOL power prediction using the Haigis formula in eyes with stage III keratoconus. There was a discrepancy in which formulas had lowest predicted errors versus median absolute predicted errors. In eyes with stage I keratoconus, the Haigis had a lower mean predicted error (0.10 D) than the Barrett Universal II, which had a higher mean predicted error (0.39 D). However, the median absolute predicted error of the Haigis Page 7 of 13
formula (0.581 D) in eyes with stage I keratoconus was significantly higher than the median absolute predicted error by the Barrett Universal II formula (0.445 D). Similarly, in keratoconus stage II eyes, the SRK/T had a lower mean predicted error (0.36 D) than the Barrett Universal II formula (0.95 D) but had a higher median absolute predicted error (0.991 D) than the Barrett Universal II formula (0.445 D). Both these findings stem from the Haigis and SRK/T formulas having positive and negative predicted errors which were higher in magnitude than the Barrett Universal II formula. These predicted errors that straddle zero negate one another when calculating predicted error, resulting in a predicted error closer to zero, but an increased median absolute predicted error. Thus, although the Haigis and SRK/T formulas seem to perform better based on mean predicted error, the Barrett Universal II formula results in errors that are lower in magnitude and is the superior formula in stage I and stage II keratoconic eyes. To our knowledge, there have not been previous studies that have showed that the Barrett Universal II formula provides the lowest predicted error and highest percentage of eyes with a predicted error within ± 0.5 D. Savini et al.9 found that the SRK/T formula was superior to the Barrett Universal II formula based on both these measures. One possible source of this difference may stem from differences in characteristics between the sample of eyes in their study and in this study that influence which formula performs better. In the study by Savini et al.,9 34.1% of eyes had axial lengths longer than 26.0 mm; however, only 26.0% of our study sample had eyes with axial lengths longer than 26.0 mm. In eyes with long axial lengths, the SRK/T formula has been demonstrated as one of the most accurate formulas by Hoffer,23 and this may contribute to the reason why Savini et al.9 found that the SRK/T formula performed best in their study, while our results showed that the Barrett Universal II formula performed best. Although there are studies prior to Savini et al.9 that also have concluded that the SRK/T formula was the most accurate formula for eyes with keratoconus,2,3 these other studies did not include the Barrett Universal II formula among the formulas they assessed. Kamiya et al.2 concluded that the SRK/T formula was better than the Haigis, Hoffer Q, and Holladay I formulas; Hashemi et al.3 found that the SRK/T formula was better than the Hoffer Q and Holladay I formulas. In all three of these studies,2,3,9 there was a trend of decreasing formula accuracy with increasing keratoconus severity, and this finding is also reflected in our results. Other studies have found that IOL formulas in general do not perform well in eyes with keratoconus. Savini et al.9 found that the percentage of eyes with a predicted error within ± 1.0 D was between 43.90% to 60.98% depending on the formula used. Similarly, Leccisotti5 showed that in eyes where IOL powers were calculated using the Holladay II formula, only 47% had a defocus equivalent within ± 1.0 D one year after surgery. Watson et al.7 reported that 60% of eyes with stage I keratoconus with an IOL power calculated using the SRK/T formula, had a predicted error within ± 1.0 D. These figures are similar to our series, which had predicted errors within ± 1.0 D in 57% to 66% of eyes depending on the formula used. Compared to normal eyes, this level of accuracy is considerably lower, with a study by Melles et al.15 showing 95.0% to 97.8% of eyes achieving predicted error within ± 1.0 D and 69.6% to 80.8% of eyes having a predicted error within ± 0.5 D depending on the formula used. With the current formulas, IOL power calculation in eyes with keratoconus still remains inaccurate relative to IOL power calculation in normal eyes. Page 8 of 13
One limitation of this study is its retrospective nature. The study was performed across multiple satellite locations, each of which used different optical biometers, and surgery was performed by different surgeons. There also were multiple IOL models implanted. These limitations prevented optimization of formula constants. Instead, constants published on the ULIB website were used, which is more in line with real clinical scenarios but not best practice for the purpose of comparing formula accuracy.24 Additionally, we did not exclude eyes that had a previous history of crosslinking; thus, having both eyes that had undergone the crosslinking procedure and eyes that had not may confound the results. Eyes that had intracorneal rings were excluded from this study; thus, these results are not able to be applied to keratoconic eyes with intracorneal rings. Eyes that had a previous history of keratomileusis, such as LASIK or PRK, were also excluded, so these results are also not able to be generalized to postlaser surgery corneal ectasia. The results of this study are also constrained to eyes with post-operative BSCVA of 20/40 or better. Keratoconus can cause significant impact on visual acuity resulting in BSCVA worse than 20/40, and these eyes may have a greater post-operative refractive error. Thus, IOL power formula errors may actually be worse when considering the overall population of keratoconic eyes which undergo cataract surgery. Finally, this series had a small sample size of eyes with stage III keratoconus, which limits the power of this study within the keratoconus stage III population. In summary, our results show that the Barrett Universal II formula performed best in the eyes in which it can be applied. All formulas had a tendency toward hyperopic errors, which may result from overestimation of corneal power by optical biometers. Generally, patients tolerate myopic errors better than hyperopic errors; thus, clinicians should take into consideration that current formulas tend to result in hyperopic errors in eyes with keratoconus. It is important to manage patient expectations in increasingly severe stages of keratoconus because predicted error increases significantly with more advanced keratoconus. Given that only 39% to 52% of eyes with mild keratoconus achieve a predicted error within ± 0.5 D depending on the formula used, managing expectations of spectacle independence is also important. Overall, there is room to improve current formulas to better predict IOL powers in eyes with keratoconus, and future research is required to develop a single formula that performs best across the spectrum of keratoconus severity.
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Acknowledgements and Disclosures: a. The authors would like to acknowledge financial support from the Sandra and Larry Small Fund and acknowledge support for the statistical analysis from the National Center for Research Resources and the National Center for Advancing Translational Sciences (NCATS) of the National Institutes of Health through Grant Number 1UL1TR001079. b. Dr. Divya Srikumaran is a consultant for Alcon Laboratories, Inc. Dr. John Ladas is a president at Advanced Euclidean Solutions. All other authors have no financial disclosures. c. No other acknowledgements.
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References 1. Kovacs I, Mihaltz K, Nemeth J, Nagy ZZ. Anterior chamber characteristics of keratoconus assessed by rotating scheimpflug imaging. J Cataract Refract Surg. 2010;36(7):1101-1106. 2. Kamiya K, Shimizu K, Miyake T. Changes in astigmatism and corneal higher-order aberrations after phacoemulsification with toric intraocular lens implantation for mild keratoconus with cataract. Jpn J Ophthalmol. 2016;60(4):302-308. 3. Hashemi H, Heidarian S, Seyedian MA, Yekta A, Khabazkhoob M. Evaluation of the results of using toric IOL in the cataract surgery of keratoconus patients. Eye Contact Lens. 2015;41(6):354-358 4. Tamaoki A, Kojima T, Hasegawa A, Nakamura H, Tanaka K, Ichikawa K. Intraocular lens power calculation in cases with posterior keratoconus. J Cataract Refract Surg. 2015;41(10):2190-2195. 5. Leccisotti A. Refractive lens exchange in keratoconus. J Cataract Refract Surg. 2006;32(5):742-746. 6. Alio JL, Pena-Garcia P, Abdulla Guliyeva F, Soria FA, Zein G, Abu-Mustafa SK. MICS with toric intraocular lenses in keratoconus: Outcomes and predictability analysis of postoperative refraction. Br J Ophthalmol. 2014;98(3):365-370. 7. Watson MP, Anand S, Bhogal M, et al. Cataract surgery outcome in eyes with keratoconus. Br J Ophthalmol. 2014;98(3):361-364. 8. Thebpatiphat N, Hammersmith KM, Rapuano CJ, Ayres BD, Cohen EJ. Cataract surgery in keratoconus. Eye Contact Lens. 2007;33(5):244-246. 9. Savini G, Abbate R, Hoffer KJ, et al. Intraocular lens power calculation in eyes with keratoconus. J Cataract Refract Surg. 2019;45(5):576-581. 10. Hashemi H, Yekta A, Khabazkhoob M. Effect of keratoconus grades on repeatability of keratometry readings: Comparison of 5 devices. J Cataract Refract Surg. 2015;41(5):1065-1072. 11. World Medical Association. World medical association declaration of helsinki: Ethical principles for medical research involving human subjects. JAMA. 2013;310(20):2191-2194. 12. Krumeich JH, Daniel J, Knulle A. Live-epikeratophakia for keratoconus. J Cataract Refract Surg. 1998;24(4):456-463.
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13. Kane JX, Van Heerden A, Atik A, Petsoglou C. Intraocular lens power formula accuracy: Comparison of 7 formulas. J Cataract Refract Surg. 2016;42(10):1490-1500. 14. Cooke DL, Cooke TL. Comparison of 9 intraocular lens power calculation formulas. J Cataract Refract Surg. 2016;42(8):1157-1164. 15. Melles RB, Holladay JT, Chang WJ. Accuracy of intraocular lens calculation formulas. Ophthalmology. 2018;125(2):169-178. 16. Kauh CY, Blachley TS, Lichter PR, Lee PP, Stein JD. Geographic variation in the rate and timing of cataract surgery among US communities. JAMA Ophthalmol. 2016;134(3):267-276. 17. Kansal V, Schlenker M, Ahmed IIK. Interocular axial length and corneal power differences as predictors of postoperative refractive outcomes after cataract surgery. Ophthalmology. 2018;125(7):972-981. 18. Bhardwaj V, Rajeshbhai GP. Axial length, anterior chamber depth-a study in different age groups and refractive errors. J Clin Diagn Res. 2013;7(10):2211-2212. 19. Kamiya K, Iijima K, Nobuyuki S, et al. Predictability of intraocular lens power calculation for cataract with keratoconus: A multicenter study. Sci Rep. 2018;8(1):131-w. 20. Gullstrand A. Appendices II and IV. Helmholtz’s Handbuch der Physiologischen Optik. 1909;1:30-415. 21. Kamiya K, Kono Y, Takahashi M, Shoji N. Comparison of simulated keratometry and total refractive power for keratoconus according to the stage of amsler-krumeich classification. Sci Rep. 2018;8(1):1243-1. 22. Kamiya K, Iijima K, Nobuyuki S, et al. Predictability of intraocular lens power calculation for cataract with keratoconus: A multicenter study. Sci Rep. 2018;8(1):131-w. 23. Hoffer KJ. The hoffer Q formula: A comparison of theoretic and regression formulas. Journal of Cataract and Refractive Surgery. 1993;19(6):700-712. 24. Hoffer KJ, Aramberri J, Haigis W, et al. Protocols for studies of intraocular lens formula accuracy. Am J Ophthalmol. 2015;160(3):40-405.e1.
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Captions Figure 1. Corneal power measured by optical biometers compared to corneal power measured by Pentacam.
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Table 1. Patient demographics by keratoconus stage. Stage I (Km ≤ 48D)
Stage II (48D < Km ≤ 53D)
Stage III (Km > 53D)
Total
46
22
5
73
Mean age [range] (years)
64.8 [31 – 84]
65.1 [44 – 79]
66.4 [63 – 73]
65.0 [31 – 84]
Mean AL (mm) ± SD
25.00 ± 1.24
24.66 ± 2.01
25.46 ± 1.22
24.93 ± 1.51
Mean Km (D) ± SD
44.98 ± 1.50
49.15 ± 1.14
56.34 ± 2.68
47.01 ± 3.50
Mean ACD (mm) ± SD
3.58 ± 0.45
3.57 ± 0.54
3.64 ± 0.61
3.58 ± 0.48
Number of eyes (n)
ACD = anterior chamber depth; AL = axial length; Km = mean corneal power
Table 2. Mean refractive predicted error by formula and keratoconus stage. The formula with the lowest predicted error for each stage is bolded. *, †, and ‡, indicate a statistical difference (p<0.05) from the formula with the lowest predicted error (in bold) in each stage determined by post-hoc analysis with the Conover method further adjusted by the Holm Family-Wise Error Rate.
Mean ± 95% CI [95% CI] Stage I (Km ≤ 48D)
Stage II (48D < Km ≤ 53D)
Hoffer Q
0.65* [0.38 – 0.92]
1.70 [0.78 – 2.62]
4.00 [2.46 – 5.55]
SRK/T
0.12* [-0.15 – 0.40]
0.36 [-0.48 – 1.21]
2.51 [0.88 – 4.14]
†
†
Stage III (Km > 53D) ‡
‡
Holladay I
0.38* [0.11 – 0.65]
1.21 [0.34 – 2.08]
2.99 [1.19 – 4.80]
Haigis
0.10 [-0.22 – 0.42]
1.12† [0.32 – 2.08]
1.90 [-0.59 – 4.38]
†
#
Barrett
0.39* [0.10 – 0.69]
0.95 [0.10 – 1.80]
Not available
Holladay II
0.56* [0.28 – 0.84]
1.49 [0.61 – 1.37]
4.38 [2.56 – 6.20]
Km = mean corneal power
‡
Table 3. Median absolute predicted error by formula and keratoconus stage. The formula with the lowest predicted error for each stage is bolded. *, †, and ‡, indicate a statistical difference (p<0.05) from the formula with the lowest predicted error (in bold) in each stage determined by post-hoc analysis with the Conover method further adjusted by the Holm Family-Wise Error Rate.
Hoffer Q
Median Absolute Error (D) [Interquartile Range] Stage I Stage II Stage III (Km ≤ 48D) (48D < Km ≤ 53D) (Km > 53D) † ‡ 0.573* [0.844] 1.009 [1.897] 4.217 [0.855] †
SRK/T
0.615 [0.807]
0.991 [0.650]
1.741 [1.734]
Holladay I
0.645 [0.780]
1.002 [1.816]
1.962 [2.504]
Haigis
0.581* [0.979]
1.448 [1.226]
1.181 [3.511]
Barrett
0.445 [0.764]
0.445 [1.72]
Not available
Holladay II 0.580* [0.909] Km = mean corneal power
†
†
1.190 [1.931]
‡
‡
#
4.520 [0.720]
Table 4. Percent of eyes within predicted error ranges. Error within ± 0.50 D (%)
Hoffer Q SRK/T Holladay I Haigis Barrett Holladay II
Error within ± 0.75 D (%)
Error within ± 1.00 D (%)
Stage I
Stage II
Stage III
Stage I
Stage II
Stage III
Stage I
Stage II
Stage III
41 48 39 39 52
18 18 41 23 50
0 0 0 40
61 61 61 61 63
27 36 45 27 55
0 0 0 40
67 72 74 70 76
50 50 50 36 59
0 0 0 40
39
23
57
32
73
46
n/a = not available
n/a 0
n/a 0
n/a 0
Corneal Power Measured by Pentacam versus Optical Biometer Pentacam Measured Mean Corneal Power (D)
60
55
y = 0.855x + 6.4333 50 R² = 0.968
45
40
35 35
40
45
50
55
Optical Biometer Measured Mean Corneal Power (D)
60
65
Kendrick Wang is a medical student at Johns Hopkins University School of Medicine. He is on the path to becoming an ophthalmologist, and his current research interests include cataract surgery and resident education policies. He has a bachelor of science degree in Bioengineering from Stanford University. His previous research includes work done at NASA Ames Research Center in the origins of life and the application of synthetic biology to space travel.